Magnetic resonance method for forming a fast dynamic image

ABSTRACT

A novel magnetic resonance imaging method is described, wherein the object to be imaged is segmented into a region of slow variation and into a region of fast variation which defines a restrictive dynamic FOV. The object in the overall FOV is sampled in k-space with a reduction factor. The k-space sampling positions in the region of fast variation are transformed by Fourier Transformation to the spatial domain and are transformed additionally to the temporal-frequency domain. Further the positions in the temporal-frequency domain derived from the sub-sampled positions in k-space are unfolded on the basis of the spatial coil sensitivity profiles of the set of receiving coils, whereas the parts of the temporal-frequency domain related to the region of slow variation are set to zero, and the resulting data in the temporal-frequency domain is Fourier transformed to the temporal domain.

The invention relates to a magnetic resonance method for forming adynamic image from a plurality of signals acquired by an array ofmultiple receiver antennae according to the preamble of claim 1. Theinvention also relates to a magnetic resonance imaging apparatus forobtaining a fast dynamic image according to the preamble of claim 5 andto a computer program product according to the preamble of claim 6.

In magnetic resonance imaging there is a general tendency to obtainacceptable images within shorter periods of time. For this reason thesensitivity encoding method called “SENSE” has recently been developedby the Institute of Biomedical Engineering and Medical Informations,University and ETH Zürich, Switzerland. The SENSE method is based on analgorithm which acts directly on the image as detected by the coils ofthe magnetic resonance apparatus and which subsequent encoding steps canbe skipped and hence an acceleration of the signal acquisition forimaging by a factor of from two to three can be obtained. Crucial forthe SENSE method is the knowledge of the sensitivity of the coils whichare arranged in so called sensitivity maps. In order to accelerate thismethod there are proposals to use raw sensitivity maps which can beobtained through division by either the “sum-of-squares” of the singlecoil references or by an optional body coil reference (see e.g. K.Pruessmann et. al. in Proc. ISMRM, 1998, abstracts pp. 579, 799, 803 and2087). In fact the SENSE method allows for a decrease in scan time bydeliberately undersampling k-space, i.e. deliberately selecting aField-of-View (FOV) that is smaller than the object to be acquired. Fromthis undersampling fold-over artefacts are obtained which can beresolved or unfolded by the use of the knowledge of a set of distinctcoils having different coil sensitivity patterns. The undersampling canbe in either one of both phase-encoding directions.

The SENSE method is preferred for acceleration of the signal acquisitionfor magnetic resonance imaging resulting in an enormous reduction inoperating time. However, the method can only be used properly if thecoil sensitivity is exactly known. Otherwise imperfections will causefold-over artefacts (aliasing) which lead to incorrect images. Inpractice the coil sensitivity cannot be estimated perfectly and will bedependent on fluctuations in time (movement of the patient, temperatureinfluences, etc.).

Another important problem of the SENSE method is the spatially varyingnoise level in the resultant image. More specifically, the resultantimage can have regions of extremely high noise level that are due tolocal “underdetermination” of the information provided by the coilpatterns.

Another kind of undersampling may be applied in dynamic imaging as hasbeen described in T. J. Provost, SMRI 1990, Works-in-progress, abstract462. If a part of the object is known to be static, advantage can betaken from this knowledge. In the simplest case, where exactly one halfo the FOV is known to be static, k-space density can be reduced be afactor of 2. This results in folding of image data. However, exactly onepixel of the dynamic object area overlaps with exactly one pixel of astatic area. If, in whatever way the static image is known, the staticaliasing can be subtracted from the required dynamic image part. Thatstatic image can be measured beforehand, afterwards, or by shiftingk-space rows from one frame to the other, in order to reconstruct anon-aliased (but temporally blurred) image (see e.g. Madore, Glover andPelc, MRM 42. p. 813-828 (1999)).

It is an object of the present invention to achieve a furtheracceleration of imaging of the above mentioned SENSE method.

This and other objects of the invention are achieved by a method asdefined in claim 1, by an apparatus as defined in claim 5 and by acomputer program product as defined in claim 6.

The main aspect of the present invention is based on the idea that anacceleration of the SENSE method is not only feasible by increasing thenumber of recording coils but also by making use of the intrinsicknowledge of the object to be imaged.

These and other advantages of the invention are disclosed in thedependent claims and in the following description in which anexemplified embodiment of the invention is described with respect to theaccompanying drawings. Therein shows:

FIG. 1 the normal imaging of voxels in the spatial domain onto pixels inthe image domain,

FIG. 2 clusters in the spatial domain which are imaged onto a pixel inthe image domain,

FIG. 3 an apparatus for carrying out the method in accordance with thepresent invention, and

FIG. 4 a circuit diagram of the apparatus as shown in FIG. 3.

The here described method applies to dynamic MRI sequences, whether in aCartesian or non-cartesian frame (like radial or spiral). It is assumedthat at least a part of an object under study has interesting temporalfrequencies of change up to f/2, which means that a frame has to beacquired every TD=1/f seconds. The object as a whole has a size of theField-of-View (FOV), which would dictate a k-space step or density incase of non-cartesian scans of no more than Δk. Whereas it is assumedthat no acceleration techniques are used.

The region to be imaged, whether a 2D slice or a 3D volume, is segmentedinto regions of “distinct temporal variability”. This means that thereis a region of slow variation below a predetermined threshold and aregion of fast variation above said threshold. This segmentationrequires a-priori data of the object to be scanned. This data may beobtained by the anatomical knowledge of the operator or by a preliminaryscan. There are at least two types of regions. Each type ischaracterised by the expected range of temporal frequencies in thatregion. The region belonging to any given variability-type may benon-contiguous.

The acquisition sequence of the present method has the followingcharacteristics:

An undersampling in k-space by any desired reduction factor a, which maybe an integer or a non-integer number; the maximally allowable value ofa is determined by the number of acquisition coils and by the data knownfrom the object, in order to segment the FOV in a region of slow motionand in a region of fast motion. In case of 2D Cartesian imaging, whereonly one phase-encoding direction exists, the k-space distance isincreased to aΔk. With non-cartesian or 3D imaging in two phase-encodingdirections, the density of k-space samples or profiles is reduced by afactor a.

A frame-to-frame change of k-space sampling positions: the pattern ofchange is repetitive, resulting in a “crystalline structure” of thefilling of (k,t)-space. The choice of the period or repetitive patterndepends on whether we want to put more emphasis on the SENSE method forunfolding the sampled data or whether the main emphasis is on theunfolding by the segmentation or “variability-restrictive” knowledge ofthe scanned object.

The reconstruction method is essentially a SENSE reconstruction. Itcharacteristic properties are that the unfolding is not performed purelyin the spatial direction, but in a space spanning at least a spatialdimension and a temporal-frequency dimension and that the knowledge ofthe regional restrictions on the temporal frequencies is applied asinput data for the regularisation.

This is basically accomplished in the following manner:

-   1. The raw data sampled by the receiving coils is Fourier    transformed from the k-space domain to the temporal domain    (x,y,z;t). In addition this data is transformed from the temporal    domain to the temporal-frequency domain (x,y,z,ω). The last    transformation is not necessarily a Fast Fourier Transformation    (FFT) or Double Fourier Transformation (DFT), but may also be    accomplished by a limited set of digital filters.-   2. The Fourier Transformation of the sampling lattice is a    structured lattice in (x,y,z,ω)-space, i.e. sets of points of that    space mutually overlap due to the undersampling.-   3. Using SENSE, the folding in (x,y,z,ω)-space is removed. Due to    the knowledge on restricted variability of the scanned object, some    parts of the resulting (x,y,z,ω)-space are known to be zero. This    knowledge is used during the SENSE unfolding, e.g. by    regularisation. This allows for a number of folded points that    exceeds the number of receiving coils.-   4. The resulting data is Fourier transformed from the    temporal-frequency domain to the temporal domain.

As an example the above described method is applied to dynamic 2Dimaging of the cardiac region. It is assumed that there are threereceiving coils and two distinct regions: a region of 60% of the FOVexhibiting a slow motion (e.g. respiratory motion) and 40% of the FOVexhibiting rapid variations (e.g. the heart region). Further it isassumed for simplicity that the rapid region is parallel to the x-axisand that all folding or unfolding is performed in the y- orphase-encoding direction. This allows for example a speed improvement ofa factor of 5 compared with the normal or full sampling. In FIG. 1 thenormal frame in k-space is depicted, wherein the crosses represent thefull sampling and the bullets represent the undersampling of the methoddescribed above. If now the lattice of the bullets in FIG. 1 istransformed to the temporal-frequency space, the situation of FIG. 2will be obtained. In this figure the information from all positions ofthe five circles 1 will fold onto one single measurement point for eachcoil. This means that the information from these circles 1 will mutuallyoverlap. In the same manner the information from the bullets 2 and fromthe crosses 3 is also overlapped. From the knowledge or preliminarinformation of the object to be scanned it is known that some regions ofthe temporal-frequency domain or (y, ω)-space must be empty. This meansthat the full FOV is restricted to a dynamic FOV with only a limitedtemporal-frequency bandwidth, which is the empty space 5 between thedotted areas 6, which represent the slow motion parts of the scannedobject and are set to zero. Thus, in effect, only three circles 1, threecrosses 2 and two bullets 3 have to be unfolded. If there are at leastthree receiving coils, unfolding is always possible.

Therefore, the attained acceleration factor can be partly attributed tothe unfolding by the SENSE method and partly to the “knowledge ondynamics” or the information of the object to be scanned.

The apparatus shown in FIG. 3 is an MR apparatus which comprises asystem of four coils 51 for generating a steady, uniform magnetic fieldwhose strength is of the order of magnitude of from some tenths of Teslato some Tesla. The coils 51, being concentrically arranged relative tothe z axis, may be provided on a spherical surface 52. The patient 60 tobe examined is arranged on a table 54 which is positioned inside thesecoils. In order to produce a magnetic field which extends in the zdirection and linearly varies in this direction (which field is alsoreferred to hereinafter as the gradient field), four coils 53 asmultiple receiver antennae are provided on the spherical surface 52.Also present are four coils 57 which generate a gradient field whichalso extends (vertically) in the x direction. A magnetic gradient fieldextending in the z direction and having a gradient in the y direction(perpendicularly to the plane of the drawing) is generated by four coils55 which may be identical to the coils 57 but are arranged so as to beoffset 90° in space with respect thereto. Only two of these four coilsare shown here.

Because each of the three coil systems 53, 55, and 57 for generating themagnetic gradient fields is symmetrically arranged relative to thespherical surface, the field strength at the centre of the sphere isdetermined exclusively by the steady, uniform magnetic field of the coil51. Also provided is an RF coil 61 which generates an essentiallyuniform RF magnetic field which extends perpendicularly to the directionof the steady, uniform magnetic field (i.e. perpendicularly to the zdirection). The RF coil receives an RF modulated current from an RFgenerator during each RF pulse The RF coil 61 can also be used forreceiving the spin resonance signals generated in the examination zone.

As is shown in FIG. 4 the MR signals received in the MR apparatus areamplified by a unit 70 and transposed in the baseband. The analog signalthus obtained is converted into a sequence of digital values by ananalog-to-digital converter 71. The analog-to-digital converter 71 iscontrolled by a control unit 69 so that it generates digital data wordsonly during the read-out phase. The analog-to-digital converter 71 issucceeded by a Fourier transformation unit 72 which performs aone-dimensional Fourier transformation over the sequence of samplingvalues obtained by digitization of an MR signal, execution being so fastthat the Fourier transformation is terminated before the next MR signalis received.

The raw data thus produced by Fourier transformation is written into amemory 73 whose storage capacity suffices for the storage of severalsets of raw data. From these sets of raw data a composition unit 74generates a composite image in the described manner; this compositeimage is stored in a memory 75 whose storage capacity suffices for thestorage of a large number of successive composite images 80. These setsof data are calculated for different instants, the spacing of which ispreferably small in comparison with the measurement period required forthe acquisition of a set of data. A reconstruction unit 76, performing acomposition of the successive images, produces MR images from the setsof data thus acquired, said MR images being stored. The MR imagesrepresent the examination zone at the predetermined instants. The seriesof the MR images thus obtained from the data suitably reproduces thedynamic processes in the examination zone.

The units 70 to 76 are controlled by the control unit 69. As denoted bythe downwards pointing arrows, the control unit also imposes thevariation in time of the currents in the gradient coil systems 53, 55and 57 as well as the central frequency, the bandwidth and the envelopeof the RF pulses generated by the RF coil 61. The memories 73 and 75 aswell as the MR image memory (not shown) in the reconstruction unit 76can be realized by way of a single memory of adequate capacity. TheFourier transformation unit 72, the composition unit 74 and thereconstruction unit 76 can be realized by way of a data processorwell-suited for running a computer program according the above mentionedmethod.

1. A magnetic resonance imaging method for forming a dynamic image froma plurality of signals acquired by an array of multiple receiverantennae, wherein the object to be imaged is segmented into a region ofslow variation below a predetermined threshold and into a region of fastvariation above said threshold which region defines a dynamic FOV beingrestricted with respect to the overall FOV of the object to be imaged,the object in the overall FOV is sampled in k-space with a reductionfactor, which depends on the number of acquisition receiver antennae andthe segmentation of the FOV, the k-space sampling positions in thedynamic FOV are transformed by Fourier Transformation to the spatialdomain and are transformed additionally to the temporal-frequencydomain, the positions in the temporal-frequency domain derived from thesub-sampled positions in k-space are unfolded on the basis of thespatial sensitivity profiles of the array of receiver antennae, whereasthe parts of the spatial-frequency domain related to the region of slowvariation are set to zero, and the resulting data in thetemporal-frequency domain is Fourier transformed to the temporal domain.2. A magnetic resonance imaging method according to claim 1, wherein thereduction factor is an integer or non-integer number greater than
 1. 3.A magnetic resonance imaging method according to claim 10, wherein thetransformation from k-space to the temporal-frequency domain is aFourier Transformation.
 4. A magnetic resonance imaging method accordingto claim 1, wherein the transformation from k-space to thetemporal-frequency domain is accomplished by a predetermined set ofdigital filters.
 5. A magnetic resonance imaging apparatus for obtaininga dynamic image from a plurality of signals comprising means forapplying a stationary magnetic field and temporary magnetic gradientfields, an array of multiple receiver antennae for recording signals,the array of receiver antennae having a spatial sensitivity profile,means for segmenting the object to be imaged into a region of slowvariation below a predetermined threshold and into a region of fastvariation above said threshold which region defines a dynamic FOV beingrestricted with respect to the overall FOV of the object to be imaged,means for sampling the object in the overall FOV in k-space with areduction factor, which depends on the number of acquisition receiverantennae and the segmentation of the FOV, means for transforming thek-space sampling positions in the dynamic FOV by Fourier Transformationto the spatial domain and for transforming additionally to thetemporal-frequency domain, means for unfolding the positions in thetemporal-frequency space derived from the sub-sampled positions ink-space on the basis of the spatial sensitivity profiles of the array ofreceiver antennae, whereas the parts of the temporal-frequency domainrelated to the region of slow variation are set to zero, and means forFourier transforming the resulting data in the temporal-frequency domainto the temporal domain.
 6. A computer program product stored on acomputer usable medium for forming a dynamic image by means of themagnetic resonance method, comprising a computer readable program meansfor causing the computer to control the execution of: applying astationary magnetic field and temporary magnetic gradient fields,acquiring magnetic resonance signals by an array of multiple receiverantennae, whereas aliasing of the magnetic resonance image arises due tofield inhomogenities and/or undersampling in k-space, segmenting theobject to be imaged into a region of slow variation below apredetermined threshold and into a region of fast variation above saidthreshold which region defines a dynamic FOV being restricted withrespect to the overall FOV of the object to be imaged, sampling theobject in the overall FOV in k-space with a reduction factor, whichdepends on the number of acquisition receiver antennae and thesegmentation of the FOV, transforming the k-space sampling positions inthe dynamic FOV by Fourier Transformation to the spatial domain and fortransforming additionally to the temporal-frequency domain, unfoldingthe positions in the temporal-frequency domain derived from thesub-sampled positions in k-space on the basis of the spatial sensitivityprofiles of the array of receiver antennae, whereas the parts of thetemporal-frequency domain related to the region of slow variation areset to zero, and Fourier transforming the resulting data in thetemporal-frequency domain to the temporal domain.